Proper braking technique is so useful that it's worth exploring in some detail and practicing its fine points.
Front Brake vs. Rear Brake
To experience the difference between front and rear brakes, take your bike out to a flat, dry area and walk alongside it holding both handgrips. Experiment with braking to a stop at different speeds using only your front or your rear brake. The front brake stops the bike instantly; the rear brake does not. (This assumes your are riding a standard upright bike, not a recumbent or tandem.) Of course, your rear brake is more effective than this when you're riding, because it has weight on it, but this demonstrates the basic difference between front and rear.
Why is the front brake more effective?
The difference between front and rear is due to the weight transfer from back to front when riding. Consider that your brakes don't stop your bike directlythey only stop your wheels from turning, and they are equally good at that. What stops your bike is the friction between the wheel and the ground, as the wheel stops turning. That friction depends on how much weight is on the wheel when you're trying to stop.
When stopping, your momentum shifts weight off of the rear wheel and onto the front wheel, giving it more traction. (Again, assuming an upright bike, not a recumbent or tandem.) The rear wheel does not have this advantageessentially it has less weight on itand skids more easily (on dry surfaces).
How to safely use the front brake
Stopping too suddenly with the front brake can cause you to be thrown over the handlebars. Practice in a safe place and at low speeds to learn how fast you can stop without doing an "endo". See Bicycling Street Smarts for more practice suggestions.